Question

The contrapositive of $\left(p\vee q\right)\Rightarrow r$ is

• A. $r\Rightarrow \left(p\vee q\right)$
• B. $\sim r\Rightarrow \left(p\vee q\right)$
• C. $\sim r\Rightarrow \sim p\wedge \sim q$
• D. $p\Rightarrow \left(q\vee r\right)$

Answer 1

Answer: (C)

Contrapositive of $p\Rightarrow q$ is $\sim q\Rightarrow \sim p$
$\therefore$ contrapositive of $\left(p\vee q\right)\Rightarrow r$ is $\sim r\Rightarrow \sim \left(p\vee q\right)$ i.e. $\sim r\Rightarrow \left(\sim p\wedge \sim q\right)$ .